God's promise to defeat Satan (Genesis 3:15) is part of His plan for salvation. The death of Jesus on the cross, His burial and resurrection, provided the only means of restoring the relationship between God and man. It is only by acknowledging this to God, asking for forgiveness, recognizing our own inability to move beyond rebellion against Him, that we can become a 'new creation' and begin a path of discipleship.
The serpent is prominently featured in a foreshadowing of this. Numbers 21:4-9 gives us the story of impatient Israelites complaining against God's provision as they traveled from Mount Hor to the Red Sea. God sent venomous serpents among them, and many people died before they begged Moses to intervene and admitted their guilt. God told Moses to create a bronze serpent and place it on a pole. Anyone who was bitten by a snake, but turned his eyes on the bronze serpent, would live.